On \(n\)-normed spaces
type: Item
instance of: scholarly article
title: On \(n\)-normed spaces
zbMATH Open document ID: 1006.46006
DOI: 10.1155/S0161171201010675
author: Hendra Gunawan
author: Mashadi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-03-12T00:00:00Z
full work available at URL: https://eudml.org/doc/49797
review text: Summary: Given an \(n\)-normed space with \(n\geq 2\), we offer a simple way to derive an \((n-1)\)-norm from the \(n\)-norm and realize that any \(n\)-normed space is an \((n-1)\)-normed space. We also show that, in certain cases, the \((n-1)\)-norm can be derived from the \(n\)-norm in such a way that the convergence and completeness in the \(n\)-norm is equivalent to those in the derived \((n-1)\)-norm. Using this fact, we prove a fixed point theorem for some \(n\)-Banach spaces.
Mathematics Subject Classification ID: 46A70
Mathematics Subject Classification ID: 46A19
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B99
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1740550
zbMATH Keywords: \(n\)-normed space
zbMATH Keywords: fixed point theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1740550